Design-Based Research for Developing and Refining Differential Calculus Instructional Lesson (DCIL)

Malaysian students often struggle with the abstract and complex concepts of calculus, primarily due to a weak foundational understanding of functions, which is a fundamental element in learning calculus.Traditional teaching methods in Malaysia further make worse this issue by emphasizing computational procedures over conceptual understanding.Addressing these challenges, this study aims to design and refine a Differential Calculus Instructional Lesson to enhance students' understanding.Using a design-based research methodology, the study followed three phases: preparation and design, teaching experiment, and retrospective analysis with intervention refinement.In the first phase, a diagnostic test identified students' specific difficulties related to graphs and graphing in differential calculus.A teaching experiment was then conducted in a pre-university class, where data were gathered through classroom observations, students' work on the Desmos platform, and interviews with a teaching witness.Analysis revealed that the instructional lesson effectively provided visual aids that aided learning, but most students only attained a basic, Action-level understanding of graphs and graphing.The retrospective analysis highlighted key areas for improvement.The lesson's extensive content within a two-hour session limited deep learning.To address this, two refinements were introduced, which are introducing a draft box feature for students to comfortably draft their answers and a narrowed focus on linear and quadratic graphs and their derivatives.These adjustments aimed to align the lesson with students' cognitive load and time constraints.This study contributes valuable insights into the application of design-based research for developing effective educational interventions.The refinement phase demonstrated the need to align instructional content with students' learning capacities.Findings offer practical guidance for educators and instructional designers on integrating theoretical frameworks into design-based research cycle and teaching strategies, ultimately address learning gaps and promote conceptual understanding in differential calculus.